Abstract
In this article, a (3+1)-dimensional variable coefficients coupled nonlinear Schrö-dinger equation is analysed with the unified method, the improved F-expansion method with Riccati equation and the modified Kudryashov method. The polynomial solutions are investigated and classified into three categories including complex solitary wave solutions, complex soliton wave solutions and complex elliptic wave solutions by applying the unified method. Besides, the physical insights of polynomial solutions are graphically discussed with suitable parameters. The complex wave solutions are derived by the improved F-expansion method with Riccati equation which contain the complex hyperbolic trigonometric solutions, complex trigonometric solutions and complex rational solutions. Lastly, the modified Kudryashov method is applied to obtain the complex wave solutions.
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